It is often too easy to dismiss a large swath of modern day pure math results as abstract nonsense. In fact, the latter phrase has been officially coined to stand for certain spectral sequential operations that are commonly deployed in algebraic topological calculations. Category theory, for instance, has been perennially criticized by some for its absence of true mathematical content, as well as contaminating the research space with white noise. Category theory has also inspired many lone-wolf career mathematicians into developing their own machineries or the late Grothendieck-style proof templates, seemingly further alienating the uninitiated. Even several recent fields medalists have been objects of name-calling in certain forums. Granted, those are prolific math writers, some would argue, nonetheless their results seem so vague, ethereal, embellished by seemingly unnecessary symbols, that the values they add to human knowledge perhaps deserves some serious research itself.
These are healthy skepticisms, as is necessary for rigorous verification commonly lacking in science nowadays. They becomes dangerous, at a personal level anyway, when their perpetuation is solely based on the notion that the incomprehensible is despicable. In fact, one key foundation of modern science is the trust in the peer review system, a tradition that parallels the western politics. Another key element of the whole scientific edifice is the accumulation of intellectual faith in not only the positive advancement of useful knowledge, but also a healthy rate of growth. The latter is certainly necessary both for the public image of the scientific community, as well as to keep the practitioners from depressive thoughts. Imagine an oracle that predicts precipitating scientific output over the next century. Any wise investor of intellectual effort would probably put his eggs into arts, business, and politics. So there is an invisible market index within the scientific realm as well, which is reflected to some extent by the tech sector of the stock market, but only the tip of an iceberg. This brings back the question of whether one has the right to criticize something in science that may not have immediate utility, or any at all? For the most part, a qualified critic of highly specialized scientific work remains an even more esoteric specialist of the same field. To become one such qualified judge, one is tempted to read his eyes out into the piles of prerequisite or corequisite work. A good reader is often a half-baked scientist of any field. For some new development in mathematics research, one has the additional barrier of leap of logical deduction, as is common in research-level math expositions. These gaps are filled only after years of experience, and a tremendous amount of talent, coupled with an engaging mind that branches into calculating sprees along with the reading. These qualities are beyond what conventional scientists are expected to have, making the whole verification process a highly human one. This partially explains why math nowadays resembles art; it is not just the subject matter itself, but the interaction of human subject with the subject matter that does justice to the work being assessed. Even worse, we are seeing cases where the active engagement of the creator of the subject matter is vitally important, as in the case of the ABC conjecture. Perhaps the only way to bring math back to the scientific standard is human cloning. A younger but similar field such as computer science has not been subjected to such brain entanglement fiasco yet. Even the most quixotic theory in CS probably can still be related easily to a well-trained scientist, simply because a. the theory must be somehow related to my macbook, and b.,if it gets too esoteric, it might get absorbed into a math discipline, such as topos theory. Perhaps in a few decades, cs will follow a similar suit and become the exclusive playground of specialists, at which point the teaching the algorithm, operating systems, database, will be completely analogous to the status of calculus and linear algebra, making those who study them science historians at best. We are at an era where the explosion and implosion of creativity is unprecedented and the evolution of our collective knowledge is taking on multiple personalities, just as the Newtonian world is inevitably superseded by the quantum reality. Unfortunately it’s not enough to just pick a version and stick to the end. One must live comfortably in this mixture state and yet relate his or her results in a plain way, much like the quantum collapsing operator.